We have studied dynamical behaviour of the infinite-range Ising spin glass model with $p$ -spin interaction above and below the transition into the non-ergodic phase. The transition is continuous at sufficiently high external magnetic field. The dynamic critical exponent of the power-law decay of the autocorrelation function at the transition point is shown to decrease smoothly to zero as the field approaches the ``tricritical'' point from above; at lower fields the transition is discontinuous. The {\it slow cooling} approach is used to study the nonergodic behavior below the transition at zero external field. It is shown that the anomalous response function $Δ(t,t')$ contains $δ$ -function as well as regular contributions at {\it any} temperature below the phase transition. No evidence of the second phase transition (known to exist within the static replica solution of the same model) is found. At lower enough temperatures the {\it slow cooling} solution approaches the one known for the standard SK model.We have studied dynamical behaviour of the infinite-range Ising spin glass model with $p$-spin interaction above and below the transition into the non-ergodic phase. The transition is continuous at sufficiently high external magnetic field. The dynamic critical exponent of the power-law decay of the autocorrelation function at the transition point is shown to decrease smoothly to zero as the field approaches the ``tricritical'' point from above; at lower fields the transition is discontinuous. The {\it slow cooling} approach is used to study the nonergodic behavior below the transition at zero external field. It is shown that the anomalous response function $Δ(t,t')$ contains $δ$-function as well as regular contributions at {\it any} temperature below the phase transition. No evidence of the second phase transition (known to exist within the static replica solution of the same model) is found. At lower enough temperatures the {\it slow cooling} solution approaches the one known for the standard SK model.

arXiv:cond-mat/9506056Jun 13, 19950 citations

Non-Equilibrium Relaxation Study of Ising Spin Glass Models

之康尾関, Yukiyasu Ozeki

Jan 1, 20010 citations

Relaxation dynamics of an Ising spin glass in a transverse field

R. V. Saburova, G. P. Chugunova

PhSSDec 1, 19940 citations

Aging in two-dimensional Ising spin glasses

A. G. Schins, E. M. Dons, A. F. M. Arts +4 more

Aging of two-dimensional (2D) Ising spin glasses with short-range interactions ${\mathrm{Rb}}_{2}$ ${\mathrm{Cu}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$ ${\mathrm{Co}}_{\mathit{x}}$ ${\mathrm{F}}_{4}$ ( ${\mathit{T}}_{\mathit{c}}$ =0) is studied in the critical regime via the low-frequency ac susceptibility and via the dc magnetization for x=0.22 and 0.33. After quenching to low temperatures, slow logarithmic relaxation is observed for both the in-phase and out-of-phase ac susceptibilities. Using the droplet scaling model, the spin-glass correlation length R is concluded to increase after a temperature quench as R\ensuremath{\propto}(lnt${)}^{1/\mathrm{\ensuremath{\psi}}}$, with t in units of some microscopic time. The exponent \ensuremath{\psi}=1.0\ifmmode\pm\else\textpm\fi{}0.1 compares with recent theoretical results and numerical simulations for 2D short-range Ising spin glasses. The waiting-time dependence found for the field-cooled and zero-field-cooled dc magnetizations points to a markedly slower crossover from the quasiequilibrium to the nonequilibrium regime than in 3D. From experiments with different cooling histories, finally, the equilibrium spin-glass state is inferred to be strongly dependent on the temperature.Aging of two-dimensional (2D) Ising spin glasses with short-range interactions ${\mathrm{Rb}}_{2}$${\mathrm{Cu}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$${\mathrm{F}}_{4}$ (${\mathit{T}}_{\mathit{c}}$=0) is studied in the critical regime via the low-frequency ac susceptibility and via the dc magnetization for x=0.22 and 0.33. After quenching to low temperatures, slow logarithmic relaxation is observed for both the in-phase and out-of-phase ac susceptibilities. Using the droplet scaling model, the spin-glass correlation length R is concluded to increase after a temperature quench as R\ensuremath{\propto}(lnt${)}^{1/\mathrm{\ensuremath{\psi}}}$, with t in units of some microscopic time. The exponent \ensuremath{\psi}=1.0\ifmmode\pm\else\textpm\fi{}0.1 compares with recent theoretical results and numerical simulations for 2D short-range Ising spin glasses. The waiting-time dependence found for the field-cooled and zero-field-cooled dc magnetizations points to a markedly slower crossover from the quasiequilibrium to the nonequilibrium regime than in 3D. From experiments with different cooling histories, finally, the equilibrium spin-glass state is inferred to be strongly dependent on the temperature.

Physical review. B, Condensed matterDec 1, 199318 citations

Ordering temperature of the infinite-range ±JIsing spin glass

Ian A. Campbell

The spin glass susceptibility of ``infinite-range'' \ifmmode\pm\else\textpm\fi{}J Ising spin glass samples has been measured as a function of sample size and temperature using numerical simulations. A slow-cooling annealing schedule was used. The data indicate that spin glass order appears to set in only at a temperature well below T=1, the accepted theoretical ordering temperature ${\mathit{T}}_{\mathit{g}}$ for the infinite-range Ising spin glass model.The spin glass susceptibility of ``infinite-range'' \ifmmode\pm\else\textpm\fi{}J Ising spin glass samples has been measured as a function of sample size and temperature using numerical simulations. A slow-cooling annealing schedule was used. The data indicate that spin glass order appears to set in only at a temperature well below T=1, the accepted theoretical ordering temperature ${\mathit{T}}_{\mathit{g}}$ for the infinite-range Ising spin glass model.

Physical Review LettersJun 1, 19925 citations

Slow cooling dynamics of the Ising

p

-spin interaction spin-glass model

We have studied dynamical behaviour of the infinite-range Ising spin glass model with

p

-spin interaction above and below the transition into the non-ergodic phase. The transition is continuous at sufficiently high external magnetic field. The dynamic critical exponent of the power-law decay of the autocorrelation function at the transition point is shown to decrease smoothly to zero as the field approaches the ``tricritical'' point from above; at lower fields the transition is discontinuous. The {\it slow cooling} approach is used to study the nonergodic behavior below the transition at zero external field. It is shown that the anomalous response function

Δ(t,t')

contains

δ

-function as well as regular contributions at {\it any} temperature below the phase transition. No evidence of the second phase transition (known to exist within the static replica solution of the same model) is found. At lower enough temperatures the {\it slow cooling} solution approaches the one known for the standard SK model.

Aging of two-dimensional (2D) Ising spin glasses with short-range interactions

{\mathrm{Rb}}_{2}

${\mathrm{Cu}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$

{\mathrm{Co}}_{\mathit{x}}

{\mathrm{F}}_{4}

(

{\mathit{T}}_{\mathit{c}}

=0) is studied in the critical regime via the low-frequency ac susceptibility and via the dc magnetization for x=0.22 and 0.33. After quenching to low temperatures, slow logarithmic relaxation is observed for both the in-phase and out-of-phase ac susceptibilities. Using the droplet scaling model, the spin-glass correlation length R is concluded to increase after a temperature quench as R\ensuremath{\propto}(lnt${)}^{1/\mathrm{\ensuremath{\psi}}}$, with t in units of some microscopic time. The exponent \ensuremath{\psi}=1.0\ifmmode\pm\else\textpm\fi{}0.1 compares with recent theoretical results and numerical simulations for 2D short-range Ising spin glasses. The waiting-time dependence found for the field-cooled and zero-field-cooled dc magnetizations points to a markedly slower crossover from the quasiequilibrium to the nonequilibrium regime than in 3D. From experiments with different cooling histories, finally, the equilibrium spin-glass state is inferred to be strongly dependent on the temperature.

{\mathit{T}}_{\mathit{g}}

for the infinite-range Ising spin glass model.